Dynamic reciprocating-bob rheometry

ABSTRACT

A sensor for making rheological measurements takes the form of a ferromagnetic bob alternately driven through a sample fluid in opposite directions by magnetic force from two alternately driven coils. The bob&#39;s position affects the mutual inductance between the coils, so it can be inferred by sensing the signal that current flowing in one coil induces in the other, and rheological properties are determined from the relationships among the bob&#39;s motion, the coil current, and the sensor geometry. Some such measurements&#39; accuracies are enhanced by computing bob acceleration and suppressing inertial effects thereby detected.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention concerns measurements of viscosity and relatedfluid properties. It finds particular application in uses of sensorsthat employ reciprocating magnetically driven bobs.

2. Background Information

Fluids' theological characteristics have been subjects of study for wellover a century, and measurements have for nearly as long been made inlaboratories routinely to characterize fluids that have been newlydeveloped or encountered. Instruments used for this purpose usuallyemploy some rotated cylindrical member to subject the fluid of interestto shearing, and various theological properties are inferred from thefluid's resistance to such shearing at various cylinder speeds. Examplesof the characteristics that such instruments determine are whether thefluid is Newtonian, what its shear sensitivity is, what its relationshipis between shear stress and shear rate, what its yield stress is, andwhether it is complex in the sense that its viscosity drifts withextended exposure to shearing.

Such methods of rheological-characteristic determination have provedquite effective and accurate, but there are a range of applications inwhich they have not proved very practical. Some research, for example,involves screening large numbers of fluids that are expensive toformulate. The expense of some such fluids has tended to dissuaderesearchers from screening them.

SUMMARY OF THE INVENTION

But I have recognized that such a barrier is greatly lowered by applyingto such theological measurements a type of sensor apparatus that hasbeen used for decades to perform industrial viscosity measurements.

That type of sensor is exemplified by the device described in U.S. Pat.No. 4,864,849 to Wright. A ferromagnetic bob is driven alternately inopposite directions by two coils through a bob channel that contains thefluid to be measured. Drive current flowing through one of the coilsdraws the ferromagnetic bob through the path in one direction. The bob'smovement causes a change in the mutual inductance between the two coilsand therefore in the amplitude of the signal induced in the other of thecoils by an AC component in the first coil's drive current. Bymonitoring that signal's amplitude, circuitry can determine when the bobhas reached a predetermined point in its travel. The circuitry can thenswitch the coils' functions so that the erstwhile driving coil becomesthe sensor coil and vice versa, and the bob therefore switchesdirection. Since the geometry of the bob and the channel within which ittravels are known, as is the force with which the coils drive the bobthrough that channel, the fluid's viscosity can be computed from thetime taken by the bob to traverse the bob path.

Such sensors' low cost, ruggedness, and simplicity, such sensors havemade it practical to monitor the properties of fluids as diverse asprinting ink, hydraulic fluid, and paint so as, for example, to enabletheir characteristics to be adjusted automatically or to triggerautomatic replacement at economically optimum intervals. But I have nowrecognized that another characteristic of this type of sensor makesadditionally applying it to other theological measurements particularlyadvantageous: it can be employed on samples small enough to make itpractical to screen fluids that are too expensive to screen withconventional laboratory instruments.

Additionally, I have made an advance in the way in which this sensortype of sensor makes measurements. Conventionally, the bob velocity onwhich computations of viscosity are based is determined by measuring thetime required for the bob to reach a predetermined position asindicated, for example, by the detection-coil amplitude's falling tosome predetermined fraction of its peak value. Since this type ofsensor's basic design allows it to be provided in a wide range ofgeometries, automatic monitoring of critical process variables has inthe past been made possible by simply selecting a combination of bobsize and bob-channel dimensions that best matches the subject fluid'stypical viscosity. I have now recognized, though, that a givenindividual sensor's range can be extended as a practical matter bymaking a subtle but significant change in the measurement technique.

Specifically, the approach I have devised bases the velocitydetermination (or computation of other velocity-related quantities) onposition values inferred from the detection coil's output atpredetermined times. As will be explained below, one of this approach'sadvantages is that it can be employed in such a fashion as todiscriminate between data taken in portions of the path from whichviscosity can be inferred with relative accuracy and data taken inportions from which velocity inferences would tend to be less accurate.As will also be explained in more detail below, using this approach totake multiple position measurements within a single traversal of the bobpath can enable the sensor's range to be extended even withoutdiscriminating between the bob path's high-accuracy and low-accuracymeasurements' positions.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a simplified cross-sectional view of one type ofreciprocating-bob sensor's coil-and-bob assembly.

FIG. 2 is a block diagram of the sensor's circuitry.

FIGS. 3A and 3B (together, “FIG. 3”) form a flow chart of a routine thatthe sensor uses to determine a fluid's shear dependence.

FIG. 4 is a plot of the sensor's sensor-coil output as a function of bobtravel.

FIGS. 5A and 5B (together, “FIG. 5”) form a flow chart of a routine thatthe sensor uses to determine shear-rate sensitivity.

FIG. 6 is a graph containing viscosity-vs.-shear-rate plots that resultfrom different shear-rate sequences applied to a fluid that exhibitsshear memory.

FIG. 7 is a typical plot of shear stress as a function of shear rate.

FIG. 8 is a flow chart of a routine that the sensor uses to detect fluidcomplexity.

FIGS. 9A and 9B (together, “FIG. 9”) are a flow chart of a routine thatthe sensor uses to determine a fluid's yield stress.

FIGS. 10A and 10B (together, “FIG. 10”) form a flow chart of a routinethat the sensor uses to measure viscosity.

DETAILED DESCRIPTION OF AN ILLUSTRATIVE EMBODIMENT

FIG. 1 is cross-sectional view of one type of sensor that can employ thepresent invention's teachings. The sensor 10 is largely cylindrical andincludes two separately driven coils 12 and 14 displaced axially fromeach other and isolated by a housing 16 from the liquid whose viscosityor other property is to be measured. But fluid is allowed to flow into acentral sample well 18 at whose mouth is located a bob-retention spider20, which confines a ferromagnetic bob 22 to the well 18. Alternatelydriving the two coils 12 and 14 causes the bob 22 to reciprocate againstthe sample liquid's viscous drag.

FIG. 2 depicts control circuitry for achieving that result. Amicroprocessor 24 controls an AC-signal generator 26 to cause it toproduce an AC signal that an adder circuit 28 adds to a DC signal from amicroprocessor-controlled digital-to-analog converter 30. The resultantadder-28 output is a low-level AC voltage superimposed on a DC voltagewhose level the microprocessor dictates. Filter 28 applies its output toa high-output-impedance current driver 32, i.e., a driver whose outputcurrent is determined by the driver's input largely independently of theload through which that current is driven. A switch 34 controlled by themicroprocessor determines whether the current from driver 32 is appliedto coil 12 or coil 14.

Microprocessor 24 operates a second switch 36 complementarily to switch34: when switch 34 applies the current to coil 12, switch 36 applies toan AC-to-DC converter 38 a signal that mutual inductance between coils12 and 14 causes in coil 14 in response to the drive current's ACcomponent. An analog-to-digital converter 40 applies to themicroprocessor 24 a digital representation of AC-to-DC converter 38'soutput, which is a DC voltage proportional the amplitude of theswitch-36-forwarded AC signal.

The analog-to-digital converter 40 applies those digital amplitudevalues to the microprocessor 24 periodically, multiple times during asingle bob stroke. When the bob has reached a predetermined point inthat stroke, the microprocessor changes the states of the switches 34and 36 so that coil 14 is the one that is driven and coil 12 is the onewhose voltage is sensed.

One type of measurement that such a circuit can be used to make is asimple fluid-characterization measurement. This measurement's purpose isto discriminate between Newtonian fluids and non-Newtonian fluids aswell as between non-Newtonian fluids that are pseudoplastic and thosethat are dilatent.

It will be recalled that absolute (dynamic) viscosity is given by:

$\begin{matrix}{{\eta = \frac{\sigma}{r_{s}}},} & (1)\end{matrix}$

where η is viscosity, σ is shear stress (shear force per unit area), andr_(s) is shear rate (velocity change per unit distance perpendicular tothe shear direction).

A fluid is Newtonian if that viscosity is independent of the shear rate,it is pseudoplastic (“shear-thinning”) if viscosity decreases withincreasing shear rate, and it is dilatent (“shear-thickening”) if itsviscosity increases with increasing shear rate.

The illustrated system employs the FIG. 3 routine to discriminate amongthe three fluid types. As that drawing's block 46 indicates, the systemis initialized before the first stroke by choosing one of the coils asthe drive coil, choosing the other as the detection coil, and adoptingas the initial drive-current level the lower of two levels that will beused in characterizing the sample fluid.

As block 48 indicates, the system then begins driving current throughthe drive coil at the selected drive level. As that block alsoindicates, the system starts the timer that will be used in determiningrelative viscosity, and it starts taking samples of the detection coil'ssignal amplitude.

Bob-position changes that result from the magnetic force that the coilcurrent causes tend to change the mutual inductance between the coils,with the result that the detection-coil amplitude is a function of bobposition. FIG. 4 gives an example of such a function. As that drawingshows, the amplitude initially increases as the bob travel begins.Eventually, though, it reaches a peak, which the loop represented byFIG. 3's blocks 50 and 52 detects. As block 54 indicates, the routinethen proceeds to identify an end point in the bob travel by determiningwhen the detection-signal amplitude has fallen below a predeterminedfraction of the peak thus detected.

When the system thereby concludes that the bob has reached its endpoint, the system reads the timer to determine how long the bob took toreach that point, and it infers the fluid's viscosity from that timervalue. In the illustrated embodiment, it draws that inference by usingthe combination of drive level and travel time to address a look-uptable (stored, for example, in a data-storage device represented by FIG.2's block 55) that contains corresponding viscosity values. These valueswill typically have been obtained by calibrating the system with variousfluids of known viscosities. Some embodiments may interpolate betweenstored values to increase resolution. Other embodiments may dispensewith the look-up table entirely; the calibration may instead have beenused to arrive the parameters of, say, best-fit polynomialapproximations to the observed calibration data, in which case theresultant polynomial determined for the chosen drive level would be usedto calculate the viscosity from the travel time. (Of course, someembodiments may use formulas that are not polynomials and/or that arefunctions of two or more variables—e.g., drive level and traveltime—rather than just one.)

Now, the FIG. 3's overall purpose is to take viscosity measurements attwo different levels of drive current and therefore shear rate and tocompare the results to determine whether the fluid is Newtonian. Insteadof simply taking as the low-shear-rate viscosity value the result of theblock-56 operation's first occurrence, the illustrated embodiment takesseveral such measurements. As block 58 indicates, that is, it determineswhether it has taken enough low-shear-rate measurements. If it has not,it takes another measurement. To that end, it switches coils: as block60 indicates, it adopts the erstwhile detection coil as the new drivecoil and the erstwhile drive coil as the new detection coil. As thatblock also indicates, the system would typically turn off the drivecurrent before making the switch. The measurement operation is thenrepeated with the bob traveling in the other direction, and suchswitching continues until enough low-shear-rate viscosity measurementshave been made.

As blocks 62 and 64 indicate, the system then adopts a high-shear-ratecurrent as the level with which to drive the coil, and severalmeasurements are taken at the high shear rate.

As block 66 indicates, the system then takes respective averages of thehigh- and low-shear-rate measurements, which it compares. As blocks 68,70, and 72 indicate, the system concludes that the fluid isNewtonian—and generates an output indicative of that conclusion on,e.g., FIG. 2's display 44—if the two averages differ by less than apredetermined tolerance value. As blocks 74, 76, and 78 indicate, on theother hand, the output displayed by the system indicates that the fluidis pseudoplastic if the high-shear-rate average is less than thelow-shear-rate average by more than the tolerance, and it indicates thatthe fluid is dilatent if the high-shear-rate average exceeds thelow-shear-rate average by more than that tolerance.

There are a number of applications in which it is desirable to know notonly whether the fluid is Newtonian, pseudoplastic, or dilatent but alsothe degree to which a pseudoplastic or dilatent fluid exhibits thatcharacteristic. There are a number of figures of merit conventionallyemployed to express the degree to which a fluid exhibits such acharacteristic, and FIG. 5 is a flow chart of a routine for employingone of them. This particular routine is based on the observation thatmany fluids' behaviors are well approximated by the following power-lawrelationship between viscosity and shear rate in theirhighest-viscosity-variation regimes:

η=K{dot over (γ)} ^(n-1),  (2)

where η is viscosity K is a constant coefficient, {dot over (γ)} is theshear rate, and n is the so-called sensitivity factor. If thesensitivity factor n is unity, the fluid is Newtonian. If 0<n<1, thefluid is shear-thinning, i.e., pseudoplastic. If n>1, the fluid isshear-thickening, i.e., dilatent.

The FIG. 5 routine's operations 84-98 will be recognized as essentiallythe same as corresponding operations in the FIG. 3 routine with theexception that, instead of being chosen from only two values, thecoil-current level adopted in step 84 is chosen from a larger number,and an average viscosity value is determined for each of that largernumber of drive—and therefore shear-rate—levels. As blocks 100, 102, 104and 106 indicate, the system steps through measurements at those levelsand then turns the coil current off.

Block 108 represents determining the shear sensitivity from theresultant observed relationship between average viscosity and shear rateby finding the value of n that yields the best fit of the above-statedpower-law relationship to the measured average-viscosity values. Indoing so, it uses the relationship between shear rate and elapsed timethat the sensor's geometry dictates. As block 110 indicates, the systemgenerates an appropriate output to represent that calculation's result.

As was stated above, the power-law relationship tends to apply to onlythe fluid's highest-viscosity-variation regime, so the operationrepresented by block 108 may include identifying that regime bycomparing the viscosity values that result from successive drive levels.The curve-fitting operation would then be applied to that regime. Otherembodiments may instead identify that regime by preceding the block-84operation with initial viscosity measurements taken at widely spaceddrive levels, in which case the drive levels chosen in the block-104operation can be restricted to those in the power-law regime.

In any event, the output generated in the block-110 operation can takeany of a wide variety of forms. For example, it may simply be thenumerical value of the shear sensitivity n itself. It could be thatvalue together with an indication, in terms of, say, the shear-raterange, of the regime in which the determined power-law relationshipprevails. Yet another type of output may be a plot of viscosity as afunction of shear rate, possibly in addition to one or both of thenumerical values mentioned above.

Particularly in the latter connection it is sometimes instructive totake into account the fact that some fluids exhibit a shear-rate“memory”: the viscosities that they exhibit can depend on the shearrates that they have recently experienced. One way to take this intoaccount is to perform the FIG. 5 operation twice, once inincreasing-drive-level order and once in decreasing-drive-level order,and to produce an output plot that shows the resultant “hysteresis,”which FIG. 6 illustrates.

By a slight change, the approach described by reference to FIG. 5 fordetermining shear sensitivity can also be used to provide an outputindicative of shear stress as a function of shear rate to produce, say,a graphical output such as that which FIG. 7 depicts. Specifically, theoperation of FIG. 5B's block 108 can be replaced with one in which shearstresses are computed for respective rates from that routine's previousmeasurements.

Since known-viscosity fluids were used to arrive at the illustratedembodiment's look-up-table or algorithmic relationship between viscosityand the combination of drive level and travel time, those knownrelationships can be used to obtain viscosity in FIG. 5A's block-94operation as an intermediate value, and the shear stress can becalculated as the product of shear rate and the thus-determinedviscosity. Of course, some embodiments may instead obtain shear stressmore directly, without the intermediate viscosity computation; therelationship between shear stress and coil current can be obtained fromthe sensor geometry and relationships (typically determined during acalibration operation) between coil current and resultant magnetic forceon the bob.

Another type of measurement that reciprocating-bob sensors can be usedfor is the detection of fluid complexity, i.e., of the tendency of afluid's viscosity to change with time when it is being sheared. FIG. 8depicts an approach that can be used for that purpose. This measurementwould likely be made over a relatively extended time period; a durationsof half an hour may be used, for instance. As block 112, indicates,therefore, the operation's initialization includes setting a “longtimer” intended for such durations. The operations that blocks 114, 116,118, 120, 122, and 124 represent will be familiar from previous routinesas the operations by which the system causes the bob to reciprocate andmake viscosity determinations based on its motion. Block 126 indicatesthat this reciprocation and viscosity measurement continue until thelong timer has timed out. Typically, this measurement is made with thesame drive-current level on each stroke.

As block 128 indicates, the system then generates an output that tellswhether shearing has caused drift in the fluid's viscosity. In theillustrated embodiment, that is done by presenting as a graphical outputa plot of filtered viscosity values as a function of time. The filter isused for noise suppression and may, for instance, produce theviscosity's exponential average. Other embodiments may instead oradditionally state whether the fluid is complex or not, basing thatdetermination on whether a detected change exceeds some threshold, and,if it is complex, whether it is rheopectic (thickening over time) orthixotropic (thinning over time).

The reciprocating-bob sensor can also be used to determine yield stress.Some fluids do not flow until they are subjected to a threshold stress,and FIG. 9 depicts one routine for determining that threshold. Block 130represents initialization for the routine as a whole, while block 132represents initialization for a single stroke. As block 132 indicates,the drive current is initially zero, and, as blocks 134, 136, 138, and140 indicate, it increases incrementally with a rest interval betweenincreases until the detection coil's signal indicates that the bob hasmoved from the initial position. Once that motion has been detected, thesystem keeps driving the bob in the same direction (with, in theillustrated embodiment, the same drive current) until it reaches theend-of-stroke position as determined in an operation that block 142represents. As blocks 144, 146, and 148 indicate, the system repeatsthis operation, inferring yield stress from the current that was appliedwhen initial movement was detected and averaging the result withprevious measurements, until some predetermined number of suchmeasurements have been made. As block 150 indicates, the routine thengenerates an output indicating the average yield-stress value, although,as block 146 indicates, it may also output intermediate values, too.

The above-described routines that determine viscosity do so by timingthe bob's travel through a predetermined distance. In this respect,their uses of the sensor are similar to those that conventionalapproaches employ. In contrast, the routine of FIG. 10 determinesviscosity by measuring the distances traveled by the bob inpredetermined time increments: the measured quantity is distance ratherthan time. The particular approach that FIG. 10 employs tends extend therange of viscosities that a given sensor can be employed to measure. Itdoes this by making incremental velocity measurements: it makes multiplemeasurements in the span of the single bob stroke or less. That routinecan be used simply to make a viscosity measurement or it can be employedas a constituent of a more-elaborate theological measurement. It can,for example, be substituted for the operations of FIG. 3's blocks 50,52, 54, and 56, FIG. 5's blocks 88, 90, 92, and 94, and FIG. 8's blocks116, 118, 120, and 122.

For purposes that will become apparent, the FIG. 10 routine begins in aninitialization operation that block 152 represents. That initializationoperation includes setting a flag to a state that indicates that the bobmotion is currently in an acceleration regime rather than aterminal-velocity regime. Additionally, the system resets aterminal-velocity-measurement counter to zero, as block 152 indicates.As will be described in more detail below, that counter indicates howmany individual velocity measurements have been made in theterminal-velocity regime.

With that flag and counter set, the system begins driving the bobelectromagnetically in the manner explained above. Periodically duringthe resultant bob stroke it measures the amplitude of the detectioncoil's output signal, as block 154 indicates. By employing one of theapproaches mentioned above the system then converts the amplitudemeasurement to a position value, as block 156 indicates.

These position measurements will be used to compute velocity at variouspoints along the stroke. Of course, a velocity determination can be madefrom only two position measurements, and some embodiments may employonly two position measurements for each velocity calculation. Fornoise-suppression purposes, though, other embodiments may employ threeor more position measurements and use some type of filtering approach toarrive at a velocity value.

Since a velocity calculation requires multiple position measurements,not enough position values will be available initially. As block 158indicates, therefore, the system computes no velocity values untilenough position values have been taken. After they have, the systemcomputes a velocity for each subsequent position value, as block 160indicates, by using as position-measurement window that overlaps thewindow used for the previous velocity computation. If the fluid isrelatively inviscid, the bob may travel through a significant portion ofits stroke before it reaches its terminal velocity. The velocitiesobserved in this initial, pre-terminal-velocity portion of its strokeresult partially from inertial effects, so the accuracy of viscositydeterminations made in that regime can suffer if appropriate provisionsare not made to take those inertial effects into account.

The routine that FIG. 10 depicts employs two alternative approaches tomaking such provisions. The first is simply to avoid velocitymeasurements in that initial portion of the stroke. As was mentionedabove, the system assumes at the beginning of the stroke that the bob isin an acceleration phase, where inertia significantly affects bobvelocity. In a manner that will described below, the system thereforetests the position measurements to determine whether it should assumethat the bob has reached the terminal-velocity portion of its travelBlock 162 represents checking the flag that indicates whether the systemhas already concluded that this regime has been reached. If theterminal-velocity regime has not yet been assumed, i.e., if the flagindicates that the system has not yet concluded that the bob has reachedits terminal velocity, the sensor determines whether such a conclusionwould now be justified. As block 164 indicates, it does this bydetermining whether the just-computed velocity exceeds the previouslydetermined velocity by more than some predetermined increment. If not,the system switches the flag, as block 166 indicates, to theterminal-velocity-regime-indicating value

Once the bob has entered the terminal-velocity regime, some number ofvelocity determinations thereafter made will be the basis for aviscosity computation. To keep track of whether the requisite number ofterminal-velocity measurements have been made, the system uses acounter, which block 168 represents incrementing. As block 170indicates, the system then returns to make another of theterminal-velocity-regime measurements if the bob has not reached the endof its travel.

The end-of-travel determination can be made in the above-mentionedmanner, in which it is based on whether the detection-coil output hasfallen to a predetermined fraction of its peak value. But anotherapproach, which for some sensor arrangements is more accurate, is toobserve whether the bob has reached a hard stop, i.e., to determinewhether two successive position measurements are equal or nearly so.

In any event, the block-170 operation's conclusion will ordinarily bethat the bob has not reached the end of its travel, so the systemreturns to make a further terminal-velocity-regime measurement. Thistime, the determination represented by FIG. 5's block 162 isaffirmative, representing the system's conclusion that theterminal-velocity regime has been reached, so the system does not returnto the block-164 determination. Instead, it performs the operationrepresented block 172, in which it reads the terminal-velocity counterto determine whether enough terminal-velocity measurements have beenmade to provide a good basis for a viscosity computation. If not enoughhave, that velocity measurement is simply stored, and the system repeatsthe block-168 and -170 operations of incrementing the terminal-velocitycounter and making the end-of-travel determination. This loop continuesin most cases until the block-172 determination is affirmative, i.e.,until enough terminal-velocity-regime measurements have been made. Whenenough have, the routine performs the block-174 operation of averagingthe velocity measurements that were made in the terminal-velocityregime; the average is based only on those measurements and not on anyof the velocities that were observed during the initial, accelerationregime.

In some embodiments, the criterion applied by the block-172determination may not be a fixed number of terminal-velocity-regimevelocity measurements; the system may, for example, merely continue totake terminal-velocity-regime velocity measurements until the bobreaches the end of its stroke, and all of the measurements thus takencontribute to the average. In other embodiments, though, the criterionmay be a predetermined number so that a first viscosity (or othervelocity-related-quantity) computation can be completed before a fullstroke ends. The rest of the stroke can then be used for anothercomputation of viscosity (or, e.g., shear rate), possibly based on adifferent drive current.

As block 176 indicates, the system infers viscosity (or some othervelocity-related quantity) from the average velocity value in one of theways mentioned above. The routine ends after the block-178 operation ofgenerating an appropriate output indicative of that value. In some casesthat output will simply be a presentation on a human-readable display.In other cases it may, for instance, be provided as one constituentinput to some fluid-characteristic determination based on some number ofsuch values or on one or more such values together with values of one ormore other physical quantities.

As was mentioned above, the routine actually provides for twoalternative approaches to determining viscosity. The first one, justdescribed, is the one that is employed in situations in which theterminal-velocity regime's duration is long enough to provide enoughterminal-velocity-regime measurements for a determination of viscosityor other desired quantity. In some cases, though, the viscosity is solow that too few velocity measurements have been taken in theterminal-velocity regime. In such cases, there will eventually be anaffirmative outcome of the block-170 determination: the bob will reachthe end of its travel before enough terminal-velocity-regimemeasurements been made.

In that situation, the system employs an alternative approach, in whichit infers velocity by mathematically matching dynamic motion curves tothe position measurements that were taken during the stroke. Forexample, the system may have previously determined that the sample fluidis Newtonian. In that case, it may be assumed that the equation ofmotion will be of the form:

$\begin{matrix}{{{{m\frac{^{2}y}{t^{2}}} + {k_{g}\eta \frac{y}{t}}} = F},} & (3)\end{matrix}$

where m is the bob's mass, y is its position, k_(g) is ageometry-determined coefficient that relates the viscous drag on the bobto the fluid's viscosity η and the bob's speed, and F is the (in theillustrated embodiment, substantially constant) magnetic force on thebob. That differential equation's solution for boundary value y=dy/dt=0at t=0 is

y(t)=[t−(1−e ^(−t/τ))τ]v _(T),  (4)

where v_(T)=F/k_(g)η is the bob's terminal velocity and τ=m/k_(g)η isthe time constant with which the bob's velocity approaches v_(T).

Since the force F and coefficient k_(g) will be known, the fluid'sviscosity can be computed from the bob motion's time constant τ orterminal velocity v_(T). So all that is necessary is to use somecurve-fitting routine to find the time constant that results in the bestmatch of the observed position values to the above differential-equationsolution. One approach, for example, is to begin by assuming a trialtime constant equal to, say, the just-observed stroke time and to usethis assumed time-constant value to compute a respectiveterminal-velocity value from each of a plurality of the observed (time,position) pairs in accordance with the following equation:

$\begin{matrix}{v_{T} = \frac{y(t)}{t - {\left( {1 - ^{t/\tau}} \right)\tau}}} & (5)\end{matrix}$

If the assumed time constant is correct, each of the terminal-velocityvalues thus determined will be approximately the same. If the assumedtime constant is too low, though, they will increase with time, and theywill decrease with time if it is too high. By employing those facts, thesystem can arrive at the correct time constant, and therefore thecorrect viscosity value, by successive approximation.

By employing the present invention's teachings, a wide range oftheological measurements can be made inexpensively. The inventiontherefore constitutes a significant advance in the art.

1. A method of fluid characterization that includes: A) driving current through a first coil in such a manner as thereby to drive a ferromagnetic bob magnetically through a bob path occupied by a sample fluid and induce in a second coil by mutual inductance a resultant detection-coil signal that depends on the bob's position along the bob path; B) taking measurements of the detection-coil signal's values at a plurality of times during a single traversal of the bob path; C) determining respective bob positions from values of the detection-coil signal thus measured; D) determining a theological characteristic of the sample fluid from a plurality of the bob positions thus determined; and E) generating a characterizer output signal indicative of the theological characteristic thus determined.
 2. A method as defined in claim 1 wherein determining the theological characteristic includes computing the sample fluid's viscosity.
 3. A method as defined in claim 1 wherein determining the theological characteristic includes mitigating inertial effects.
 4. A method as defined in claim 3 wherein determining the theological characteristic includes computing the sample fluid's viscosity and mitigating inertial effects in doing so.
 5. A method as defined in claim 1 wherein determining the theological characteristic includes: A) computing a plurality of velocity values from the determined bob positions; B) classifying sequences of the measurements taken in a single traversal into acceleration and terminal-velocity regimes in accordance with comparisons of successive said velocity values; and C) basing determination of the theological characteristic from the measurements taken in the terminal-velocity regime without employing the measurements taken in the acceleration regime.
 6. A method as defined in claim 5 wherein determining the theological characteristic includes computing the sample fluid's viscosity from the measurements taken in the terminal-velocity regime without employing the measurements taken in the acceleration regime.
 7. A method as defined in claim 1 wherein: A) the method additionally includes so driving current through the second coil as thereby to drive the ferromagnetic bob magnetically back through the bob path and induce in the first coil by mutual inductance a resultant detection-coil signal that depends on the bob's position along the bob path; and B) the bob positions are additionally determined from values of the detection signal measured at a plurality of times as the bob is driven back through the bob path.
 8. A method as defined in claim 1 wherein the characterizer output signal indicates whether the sample fluid is Newtonian.
 9. A method as defined in claim 8 wherein the characterizer output signal also indicates whether the fluid is a shear-thinning or shear-thickening fluid if the characterizer output signal indicates that the fluid is not Newtonian.
 10. A method as defined in claim 1 wherein a characterizer output represents how sensitive the sample fluid's viscosity is to shear rate.
 11. A method as defined in claim 1 wherein the characterizer output represents shear stress on the sample fluid as a function of the shearing that the sample fluid undergoes.
 12. A method as defined in claim 1 wherein: A) the driving of the ferromagnetic bob through the bob path occurs repeatedly throughout a measurement duration; and B) the characterizer output signal represents the sample fluid's viscosity as a function of how long the bob has been driven repeatedly through the fluid.
 13. A fluid characterizer comprising: A) a ferromagnetic-bob-type instrument comprising: i) a sample well; ii) a ferromagnetic bob disposed in the sample well for reciprocation in first and second directions along a bob path therethrough; and iii) first and second coils so disposed with respect to the sample well that current driven though the first coil results in magnetic force that tends to drive the bob in the first direction, that current driven though the second coil results in magnetic force that tends to drive the bob in the second direction, and that mutual inductance between the coils depends on the bob's position; B) control circuitry that includes: i) driver circuitry for so driving current including an AC component through at least the first coil as to drive the bob in at least the first direction through fluid contained by the sample well; ii) sensor circuitry for sensing a signal that the AC component driven though one of the coils causes in the other of the coils by mutual inductance and for generating a sensor output representative of thereof, and iii) computation circuitry for generating from the sensor output a characterizer output that indicates at least one of a) the fluid's yield stress; b) the shear stress on the fluid as a function of the shearing that the fluid undergoes; c) whether the fluid is Newtonian; d) how sensitive the fluid's viscosity is to shear rate; and e) the fluid's viscosity as a function of how long the bob has been driven through the fluid.
 14. A fluid characterizer as defined in claim 13 wherein the characterizer output represents the fluid's yield stress.
 15. A fluid characterizer as defined in claim 13 wherein the characterizer output represents the shear stress on the fluid as a function of the shearing that the fluid undergoes.
 16. A fluid characterizer as defined in claim 13 wherein the characterizer output indicates whether the fluid is Newtonian.
 17. A fluid characterizer as defined in claim 16 wherein the characterizer output indicates whether the fluid is a shear-thinning or shear-thickening fluid if the fluid is not Newtonian.
 18. A fluid characterizer as defined in claim 13 wherein the characterizer output indicates how sensitive the fluid's viscosity is to shear rate.
 19. A fluid characterizer as defined in claim 13 wherein the characterizer output represents the fluid's viscosity as a function of how long the bob has been driven through the fluid.
 20. A fluid characterizer as defined in claim 13 wherein the driver circuitry so drives current including through the first and second coils as alternatively to drive the bob in the first and second directions through fluid contained by the sample well.
 21. A fluid characterizer comprising: A) a ferromagnetic-bob-type instrument comprising: i) a sample well; ii) a ferromagnetic bob disposed in the sample well for reciprocation in first and second directions along a bob path therethrough; and iii) first and second coils so disposed with respect to the sample well that current driven though the first coil results in magnetic force that tends to drive the bob in the first direction, that current driven though the second coil results in magnetic force that tends to drive the bob in the second direction, and that mutual inductance between the coils depends on the bob's position; and B) control circuitry that includes: i) driver circuitry for so driving current including an AC component through the first and second coils as to drive the bob in at least the first direction through a sample fluid contained by the sample well; ii) sensor circuitry for taking measurements of the values, at a plurality of times during a single traversal of the bob path, of a detection-coil signal that the AC component driven though one of the coils causes in the other of the coils by mutual inductance and for generating a sensor output representative of thereof; and iii) computation circuitry for: a) determining respective bob positions from values of the detection-coil signal thus measured; b) determining a theological characteristic of the sample fluid from a plurality of the bob positions thus determined; and c) generating a characterizer output signal indicative of the theological characteristic thus determined.
 22. A fluid characterizer as defined in claim 21 wherein determining the theological characteristic includes computing the sample fluid's viscosity.
 23. A fluid characterizer as defined in claim 21 wherein determining the theological characteristic includes mitigating inertial effects.
 24. A fluid characterizer as defined in claim 23 wherein determining the theological characteristic includes computing the sample fluid's viscosity and mitigating inertial effects in doing so.
 25. A fluid characterizer as defined in claim 21 wherein determining the theological characteristic includes: A) computing a plurality of velocity values from the determined bob positions; B) classifying sequences of the measurements taken in a single traversal into acceleration and terminal-velocity regimes in accordance with comparisons of successive said velocity values; and C) basing determination of the theological characteristic from the measurements taken in the terminal-velocity regime without employing the measurements taken in the acceleration regime.
 26. A fluid characterizer as defined in claim 25 wherein determining the theological characteristic includes computing the sample fluid's viscosity from the measurements taken in the terminal-velocity regime without employing the measurements taken in the acceleration regime.
 27. A fluid characterizer as defined in claim 21 wherein: A) the driver circuit so drives current through the second coil as thereby to drive the ferromagnetic bob magnetically back through the bob path and induce in the first coil by mutual inductance a resultant detection-coil signal that depends on the bob's position along the bob path; and B) the computation circuit additionally determines the bob positions from values of the detection signal measured at a plurality of times as the bob is driven back through the bob path.
 28. A fluid characterizer as defined in claim 21 wherein the characterizer output signal indicates whether the sample fluid is Newtonian.
 29. A fluid characterizer as defined in claim 28 wherein the characterizer output signal also indicates whether the fluid is a shear-thinning or shear-thickening fluid if the characterizer output signal indicates that the fluid is not Newtonian.
 30. A fluid characterizer as defined in claim 21 wherein a characterizer output represents how sensitive the sample fluid's viscosity is to shear rate.
 31. A fluid characterizer as defined in claim 21 wherein the characterizer output represents shear stress on the sample fluid as a function of the shearing that the sample fluid undergoes.
 32. A fluid characterizer as defined in claim 21 wherein: A) the driving of the ferromagnetic bob through the bob path occurs repeatedly throughout a measurement duration; and B) the characterizer output signal represents the sample fluid's viscosity as a function of how long the bob has been driven repeatedly through the fluid.
 33. A method of fluid characterization that includes: A) providing a ferromagnetic-bob-type instrument that includes: i) a sample well; ii) a ferromagnetic bob disposed in the sample well for reciprocation in first and second directions along a bob path therethrough; and iii) first and second coils so disposed with respect to the sample well that current driven though the first coil results in magnetic force that tends to drive the bob in the first direction, that current driven though the second coil results in magnetic force that tends to drive the bob in the second direction, and that mutual inductance between the coils depends on the bob's position; B) so driving current including an AC component through the first and second coils as to drive the bob in at least the first direction through fluid contained by the sample well; C) sensing a signal that the AC component driven though one of the coils causes in the other of the coils by mutual inductance; D) generating a sensor output representative of thereof, and E) generating from the sensor output a characterizer output that indicates at least one of: i) the fluid's yield stress; ii) the shear stress on the fluid as a function of the shearing that the fluid undergoes; iii) whether the fluid is Newtonian; iv) how sensitive the fluid's viscosity is to shear rate; and v) the fluid's viscosity as a function of how long the bob has been driven through the fluid.
 34. A method as defined in claim 33 wherein the characterizer output represents the fluid's yield stress.
 35. A method as defined in claim 33 wherein the characterizer output represents the shear stress on the fluid as a function of the shearing that the fluid undergoes.
 36. A method as defined in claim 33 wherein the characterizer output indicates whether the fluid is Newtonian.
 37. A method as defined in claim 36 wherein the characterizer output indicates whether the fluid is a shear-thinning or shear-thickening fluid if the fluid is not Newtonian.
 38. A method as defined in claim 33 wherein the characterizer output indicates how sensitive the fluid's viscosity is to shear rate.
 39. A method as defined in claim 33 wherein the characterizer output represents the fluid's viscosity as a function of how long the bob has been driven through the fluid.
 40. A method as defined in claim 33 wherein current is so driven through the first and second coils as alternatively to drive the bob in the first and second directions through fluid contained by the sample well. 